Average Error: 0.0 → 0.0
Time: 22.1s
Precision: 64
\[\frac{1}{x - 1} + \frac{x}{x + 1}\]
↓
\[\sqrt[3]{\left(\left(\frac{x}{x + 1} + \log \left(e^{\frac{1}{x - 1}}\right)\right) \cdot \left(\frac{1}{x - 1} + \frac{x}{x + 1}\right)\right) \cdot \left(\frac{1}{x - 1} + \frac{x}{x + 1}\right)}\]
\frac{1}{x - 1} + \frac{x}{x + 1}
↓
\sqrt[3]{\left(\left(\frac{x}{x + 1} + \log \left(e^{\frac{1}{x - 1}}\right)\right) \cdot \left(\frac{1}{x - 1} + \frac{x}{x + 1}\right)\right) \cdot \left(\frac{1}{x - 1} + \frac{x}{x + 1}\right)}
double f(double x) {
        double r14888590 = 1.0;
        double r14888591 = x;
        double r14888592 = r14888591 - r14888590;
        double r14888593 = r14888590 / r14888592;
        double r14888594 = r14888591 + r14888590;
        double r14888595 = r14888591 / r14888594;
        double r14888596 = r14888593 + r14888595;
        return r14888596;
}
↓
double f(double x) {
        double r14888597 = x;
        double r14888598 = 1.0;
        double r14888599 = r14888597 + r14888598;
        double r14888600 = r14888597 / r14888599;
        double r14888601 = r14888597 - r14888598;
        double r14888602 = r14888598 / r14888601;
        double r14888603 = exp(r14888602);
        double r14888604 = log(r14888603);
        double r14888605 = r14888600 + r14888604;
        double r14888606 = r14888602 + r14888600;
        double r14888607 = r14888605 * r14888606;
        double r14888608 = r14888607 * r14888606;
        double r14888609 = cbrt(r14888608);
        return r14888609;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\frac{1}{x - 1} + \frac{x}{x + 1}\]
  2. Using strategy rm

  3. Applied add-cbrt-cube0.0

    \[\leadsto \color{blue}{\sqrt[3]{\left(\left(\frac{1}{x - 1} + \frac{x}{x + 1}\right) \cdot \left(\frac{1}{x - 1} + \frac{x}{x + 1}\right)\right) \cdot \left(\frac{1}{x - 1} + \frac{x}{x + 1}\right)}}\]
  4. Using strategy rm

  5. Applied add-log-exp0.0

    \[\leadsto \sqrt[3]{\left(\left(\frac{1}{x - 1} + \frac{x}{x + 1}\right) \cdot \left(\color{blue}{\log \left(e^{\frac{1}{x - 1}}\right)} + \frac{x}{x + 1}\right)\right) \cdot \left(\frac{1}{x - 1} + \frac{x}{x + 1}\right)}\]

  6. Final simplification0.0

    \[\leadsto \sqrt[3]{\left(\left(\frac{x}{x + 1} + \log \left(e^{\frac{1}{x - 1}}\right)\right) \cdot \left(\frac{1}{x - 1} + \frac{x}{x + 1}\right)\right) \cdot \left(\frac{1}{x - 1} + \frac{x}{x + 1}\right)}\]

Reproduce

herbie shell --seed 2019104 
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))